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NOTE. — In accordance with the construction shown in Fig. 26, SPv will always lie between the vanishing point'of a system and its measure point.

99. The measure point of any system of lines is usually de noted by a small letter m with an index corresponding to its re lated vanishing point. Thus, mob signifies the measure point for the system of lines vanishing at vab.

100. The vanishing point for ab in Fig. 26 has been found at el'. The point n, PIPP, is the horizontal projection of this vanishing point. The measure point (mob) for all lines vanishing at vab will be found on VI-I, at a distance from vab equal to the distance from n to SP'S (98). In accordance with this statement, m" has been found by drawing an arc with n as center, and with a radius equal to the distance from n to SP", and dropping from the 'intersectiun of this arc with IIPP'a vertical line. m" is found at the intersection of this vertical line with VII.

101. The perspective of ab has been drawn from aP, vanishing at va". aP on VII, is made equal to the length of a"bif given in the plan of the card. A measure line through b,, vanishing at mab, will determine the length of eV. A line from bP vanishing at va", and one from c/P vanishing at vab, will intersect at cP, com pleting the perspective plan of the card. • 102. Even the vanishing points (v" and va'') for the sides of the card may be found without drawing a diagraM. Since In is drawn parallel to ab, it makes the same angle with HPP that ab makes. Similarly, is drawn parallel to ad, it makes the same angle with HPP that ad makes. The angle between fps and fit must show the true angle made by the two lines ab and ad in the diagram. Therefore, having assumed SP", we have sim ply to draw two lines through SP", making with HPP the respec tive angles that the two sides of the cards are to make with the picture plane, care being taken that the angle these two lines make•with one another shall equal the angle shown between the two sides of the card in the given plan. Thus, in Fig. 27, the two projections of the station point have first been assumed. Then through SP", two lines (f71 and fh) have been drawn, making re spectively, with IIPP; the angles (H° and N°) which it is desired the sides of the card shall make with the picture plane, care being taken to make the angle between fn and fh equal to a right angle, since the card shown in the given plan is rectangular.

Verticals dropped to VH from the points and h will deter mine vab and ed. Having found vab and vad, mab and mad should next be determined, as explained in § 98. VH, should now be assumed, and chosen at any point on this line. It is well not to assume'ar very far to the right or left of an imaginary vertical line through SPv.

From ar the sides of the card will vanish at vab and rad re spectively. Measure off from on Vhf,, to the right, a distance (aPb,) equal to the length of the side OP shown in the given plan. A measure line through b,, vanishing at ma'', will deter mine the length of etrbr. Measure off from e on V1•1„ to the

left, a distance equal to the length of the side a"d" shown in the given plan. A measure line through d, vanishing at mad, will determine the length of aPdP.

From bP and dr, the remaining sides of the card vanish to vad and vab respectively, determining. by their intersection the point cr.

- The line and"' in plan is divided by points t", s", and r".

To divide the perspective (aPdP) of this line in a similar manner, lay off on VII, from ar, to the left, the divisions s„ and r„ as taken from the given plan. Measure lines through t„ 8,, and vanishing at mad, will intersect aPdP, and determine tr, sP, and rP.

103. As has already been stated., the true length of any line is always measured on VI-I„ and from the true length, the length of the perspective projection of the line is determined by measure lines vanishing at the measure point for the line whose perspective is being determined. Care must be taken to measure off the true length of the line in the proper direction. The general rule for doing this is as follows : — If the measure point of any line is at the right of SP', the true length of the line will be laid off on in such a man ner that measurements for the more distant points in the line will be to the left of the measurements for the nearer points.

Thus, mad is at the right of SPY. The point dP is more dis tant than the point t". Therefore, the measurement for the point dP will be to the left of the measurement for the point t". In other words, since mad is to the right of SPY, which repre sents a point more distant must be to the left of the distance between and being equal to the true length of tPdr, as shown by t"d" in the given plan.

On the othei hand, if the measure point for any system of lines is to the left of SP", the true measurements for any line of the system should be laid off on Vii, in such a manner that measurements for more distant points on the line are to the right of measurements for the nearer points of the line.

Thus, WI' is to the left of S'Pv. The point bP is more distant than the point a". Therefore, b„ which shows the true measure ment for the point b', must be laid off to the right of aP.

104. It sometimes happens that a line extends in front of the picture plane, as has already been seen in the lines of the nearest corner of the porch in Fig. 22. It may be desired to extend the line aPdP in Fig. 27, in front of the picture plane, to the point yP, as indicated in the perspective projection. In this case, the point a" being more distant than the point yP, and mad being to the rt;ght of SPY, the true measurement of aryl' must be laid off on VH, in such a manner that the measurement for al' will be to the left of the measurement for y". In other words; y, must be on VH, to the right of al', the distance a"y, showing the true length of a"y".